Problem: What do the following two equations represent? $-3x-2y = -4$ $8x-12y = 1$
Solution: Putting the first equation in $y = mx + b$ form gives: $-3x-2y = -4$ $-2y = 3x-4$ $y = -\dfrac{3}{2}x + 2$ Putting the second equation in $y = mx + b$ form gives: $8x-12y = 1$ $-12y = -8x+1$ $y = \dfrac{2}{3}x - \dfrac{1}{12}$ The slopes are negative inverses of each other, so the lines are perpendicular.